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What is f plus f plus f plus f simplified?
Since f is the 6th letter of the alphabet you do 6*4 to get 24. X is the 24th letter of the alphabet . So, x is the answer
How does an equation represent a function?
An equation in this context usually has two variables, let's say x and y. A function in this case usually has one variable as an input let's say x. f(x) is the output of the expression that defines the function. There are some criteria of a function that equations do not have. Functions must only have one output per input, basically, if you draw a vertical line anywhere on the graph, the line must only intersect at one point. So how does an equation represent a function? We can use the second variable in the equation to represent the output of the function and isolate f(x) Examples: x+ 3y = 10 x + 3f(x) = 10 3f(x) = 10 - x f(x) = (10-x)/3 x+ 3y = 10 represents f(x) = (10-x)/3 Trying x^2+y^2=9 would not work, because isolating for y we would get and equation of y = (plus or minus)sqrt(9-x^2) which does not follow the criteria of a function. Hope it helped!
How do you find asymptotes?
Veritcal asymptotes are where the denominator of a fraction becomes 0 and the value of f(x) becomes undefined. Set the denominator to 0 and solve.Horizontal asymptotes are values of f(x) when x→∞ and x→-∞Two examples:f(x)=3x² / (x²+1)Vertical:Set (x²+1)=0 and solve for x.x²=-1 has no answers, so there is no vertical asymptote.Horizontal:Divide all terms by the highest power of x to eliminate unimportant valuesdividing by x², you get 3 / (1 + (1/x²))As x→∞ then 1/x² vanishes, leaving 3/1=3, so there is an asymptote at y=3f(x)=(x-3) / (x²+3x)Vertical:Set (x²+3x)=0 and solve. x={0,-3} so there are vertical asymptotes at 0 and -3Horizontal:Divide out by x²(x/x² - 3/x²) / (x²/x² + 3x/x²) as x→∞The terms in the numerator all vanish, making the answer 0, so there is a horizontal asymptote at 0.Enjoy.■A vertical asymptote also exists for the value of x (assuming a function of x) where the function becomes undefined. For instance:f(x) = ln (x). The logarithmic function is not defined for x
